We investigate sound propagation in lossy, locally resonant periodic structures by studying an air-filled tube periodically loaded with Helmholtz resonators and taking into account the intrinsic viscothermal losses. In particular, by tuning the resonator with the Bragg gap in this prototypical locally resonant structure, we study the limits and various characteristics of slow sound propagation. While in the lossless case the overlapping of the gaps results in slow-sound-induced transparency of a narrow frequency band surrounded by a strong and broadband gap, the inclusion of the unavoidable losses imposes limits to the slowdown factor and the maximum transmission. Experiments, theory, and finite element simulations have been used for the characterization of acoustic wave propagation by tuning the Helmholtz/Bragg frequencies and the total amount of loss both for infinite and finite lattices. This study contributes to the field of locally resonant acoustic metamaterials and slow sound applications.

The vibration filtering properties of a phononic crystal pipe whose unit cell consists of two segments of different materials and cross sections are studied numerically and experimentally. Such an architected bi-material pipe leads to the alignment of the dispersion branches in the same frequency ranges for all types of waves (flexural, longitudinal, and torsional), leading to an absolute bandgap. Each motion is studied by a 1D model in which the propagation of Floquet–Bloch waves in lossy media is considered. Numerical optimization is based on the simplex algorithm and aims to control both the central frequency and the bandwidth of the absolute bandgap on a selected target. Experimental characterization of a demonstrator confirms the filtering effects due to partial and absolute bandgaps even in the presence of quite high structural damping.